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Title:
Kahler-Einstein metrics on Fano manifolds II
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Abstract:
The talk will be based on joint work with Xiuxiong Chen and Song Sun. The existence of Kahler Einstein metrics in the case of negative or zero Ricci curvature was established in the 1970’s by Aubin and Yau. Yau conjectured that the existence in the positive case should be equivalent to an algebro-geometric condition of “stability”. In the 1990’s, Tian introduced a notion of K-stability and showed that it was a necessary condition. Our recent work confirms that it is also sufficient. We will explain this background and give some outline of the proof, which involves deforming through a family of metrics with cone singularities along a divisor.
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